184 
In the case of simple tones, ze. of such as possess no over- 
tones whatever, the difference between consonance and disso- 
nance depends on the presence of a class of sounds discovered 
by Sorge in 1740, and generally since known as Tartini’s tones, 
but called by Helmholtz, who has considerably increased the 
series, combination-tones. In the case of two simple tones the 
interval is consonant if no audible beats are produced by combi- 
nation-tones with the primaries or with each other—dissonant, 
if otherwise. 
Professor Tyndall, in the last of his published Lectures on 
Sound, has given a theory’of consonance which differs radically 
from that of Helmholtz, and is irreconcilably at variance with 
experiment. The fundamental error of his reasoning consists in 
the neglect of the most essential condition for the production of 
audible beats between two simple tones, namely, that they must 
lie near each other in the musical scale. 
(See for the proof of this in detail a Letter by the writer of 
this paper in ‘Nature’ for March 3, 1870.) 
Professor CHALLIS made some remarks vindicating Dr Smith 
and Young from a statement made by Prof. Tyndall, with regard 
to the theory of consonance not being understood before the 
time of Helmholtz, and expressed a general concurrence in Mr 
Taylor's paper, so far as he had followed up the subject. 
Mr TRorrer said that Helmholtz had first assigned to combi- 
nation-tones their true origin. When two loud tones coexist the 
excursions of the molecules are so large that terms of the second 
order arising from the combination of the vibrations become 
sensible. 
Mr PALEY remarked upon the beats heard when a church 
bell has been struck, and the tone is dying away; thinking 
that this might result from the tin and copper not being well 
amalgamated in the metal. 
Mr Tay or, followed by Mr Trorrer, said that these beats 
were produced by the bell not being in perfect tune throughout, 
